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arXiv · 0905.3085

A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p

Nigel P. Byott
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Abstract

Let S/R be a finite extension of discrete valuation rings of characteristic p>0, and suppose that the corresponding extension L/K of fields of fractions is separable and is H-Galois for some K-Hopf algebra H. Let D_{S/R} be the different of S/R. We show that if S/R is totally ramified and its degree n is a power of p, then any element $ρ$ of L with $v_L(ρ)$ congruent to $-v_L(D_{S/R})-1$ mod n generates L as an H-module. This criterion is best possible. These results generalise to the Hopf-Galois situation recent work of G. Elder for Galois extensions.

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Nigel P. Byott. 2011-02-07. A Valuation Criterion for Normal Basis Generators of Hopf-Galois Extensions in Characteristic p. https://arxiv.org/abs/0905.3085

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